The equation of the chord joining two points $(x_1, y_1)$ and $(x_2, y_2)$ on the rectangular hyperbola $xy = c^2$ is :

Question

( A ) $\frac{x}{x_1-x_2} + \frac{y}{y_1-y_2} = 1$
( B ) $\frac{x}{y_1+y_2} + \frac{y}{x_1+x_2} = 1$
( C ) $\frac{x}{x_1+x_2} + \frac{y}{y_1+y_2} = 1$
( D ) $\frac{x}{y_1-y_2} + \frac{y}{x_1-x_2} = 1$